Optimization

3 Credits · Level: Graduate, Undergraduate

Optimization problems arise in a variety of applied sciences. Examples are the most economical transport of goods from service points to destinations, the design of components in manufacturing, or the desire to minimize noises and vibrations in airplanes or cars. The mathematical formulation of optimization problems results in the task of minimizing or maximizing functions which are subject to additional conditions called constraints. Some optimization problems, such as finding the extreme values (maxima and minima) of continuous functions of several variables, are already discussed in calculus. Of particular interest in this course are optimization problems with constraints, possibly given by additional equations, inequalities, or differential equations. According to the type and the nature of the constraint, different techniques of solving the optimization problem are to be developed. These include linear programming, nonlinear programming, variational problems, and optimal control. Students will see a good number of examples of optimization problems, study various analytical techniques of solving them, reinforce their knowledge of differential calculus of functions of several variables, and should gain an appreciation of two fundamental mathematical concepts: Linearity and Convexity.